BTIG analyst Mark Palmer writes that "some clients have expressed concern" about "the possibility that the U.S. government will embark on a new program of tax simplification that would obviate much of the need for tax preparation assistance."

"The benefits of tax simplification have been touted by Democrats and Republicans alike for the past 50 years," he writes.

Opponents of a simplified tax code include "tax lawyers, accountants, investment advisors specializing in tax shelters, IRS agents, publishers and others in peripheral businesses," whose livelihood depends on its complexity, Palmer contends. He believes "these groups have their own small armies of lobbyists and significant sway over the legislative process."

Another consideration for H&R Block investors is what would happen if the U.S. goes over the "fiscal cliff," following a failure by Congress to agree on a plan to reduce the U.S. deficit.

Falling off the cliff would create confusion, leading to an opportunity for H&R Block to win new clients, according to Palmer.

"Confusion over taxes, such as that potentially created by the fiscal cliff, is the mother's milk of the assisted tax preparation industry, and the complexity of this year's situation could give H&R Block an edge,' he writes.